Having trouble printing black and white photography scans
Hello dear community,
My name is Oscar, I operate on MacOS and i've been working on a project for some time now which involves myself scanning some of my black and white photography from printed books, then editing them in photoshop, exporting them as cmyk images in pdf format, and then inserting them into an Indesign or Illustrator file to work on text editing and so forth, to then having them be exported again and getting them printed.
For today, I will use the following image as an example;

Here we have my file of a 'J-card', as you can see it is cmyk indicated by the blue folding lines
Here are its details:

+ here are the details of the original scan, i.e. the image which was modified and then used for the jcard:

...Now once professionally printed, below would be my two outcomes;
the top is printed in cmyk and bottom is printed in greyscale.

As you will immediately see, the top looses a little contrast and includes a purplish hue, while the bottom image simply looses a lot of contrast yet displays grayscale colors.
Now, ideally, I'd like to have the final print look as close as possible to its digital counterpart, though in the past, I've always been left with mostly green or red hues, leaving me scratching my head as to how I could better prepare my files.
It goes without saying that vector images and the likes are not affected, in other words, it has to do with the scanned images, and I would be forever thankful if someone could point me towards what I need to do or which tutorial I need to watch, in order to get the maximum out of my final prints, rather than being left with a greenish or purplish image that lacks contrast when printed in cmyk.
Thanks to anyone willing to help, I'll gladly share any needed additional information, (I've experienced this problem over multiple Ps/Id/Ai iterations).
Best,
O.
